Is my friend justified in asking for a reduction in the remaining portion of the debt due to the rising price of gold, or am I justified in refusing that?

If the debtor requests a partial waiver of his debt as an act of kindness, the creditor is not obligated to grant it. The debtor is required to repay the full debt in the same currency he borrowed, and the rise in the value of gold or whatever the debtor purchased with the money has no bearing. It is permissible for the creditor and debtor to agree on repayment in gold or another currency at the rate of the day of repayment.